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1. Hi,

I understand quadratic equations using factoring when the first factor has a coefficient of 1. e.g.

x^2 +10x + 25

I get confused when the coefficient is more than 1? e.g.

6x^2 - 8x - 8

or

2x^4 + 14x^2 + 24

I think its because both equations have a common factor?
Also, can someone explain decomposition?

Thank you
2. (Original post by x-Natalie-x)
Hi,

I understand quadratic equations using factoring when the first factor has a coefficient of 1. e.g.

x^2 +10x + 25

I get confused when the coefficient is more than 1? e.g.

6x^2 - 8x - 8

or

2x^4 + 14x^2 + 24

I think its because both equations have a common factor?
Also, can someone explain decomposition?

Thank you
Just take out whatever you need

Eg in your first example, 6x^2 - 8x - 8 can become 6(x^2 -(8x/6) - (8/6)) and factorise the inside and hen multiply the result by 6 at the end.
3. (Original post by x-Natalie-x)
Hi,

I understand quadratic equations using factoring when the first factor has a coefficient of 1. e.g.

x^2 +10x + 25

I get confused when the coefficient is more than 1? e.g.

6x^2 - 8x - 8

or

2x^4 + 14x^2 + 24

I think its because both equations have a common factor?
Also, can someone explain decomposition?

Thank you
The first thing I'd do is factor out the highest common factor amongst all the coefficients. So for I'd factor out 2 to get

Then consider factorising and the way you do it is say that it is equal to where and . One such case is and so just sub those back up in there to get the total factorisation of

In general, when you have , where a,b,c have no more common factors, it can be factorised into the form where and
4. (Original post by RDKGames)
The first thing I'd do is factor out the highest common factor amongst all the coefficients. So for I'd factor out 2 to get

Then consider factorising and the way you do it is say that it is equal to where and . One such case is and so just sub those back up in there to get the total factorisation of

In general, when you have , where a,b,c have no more common factors, it can be factorised into the form where and
Out of interest, were you taught this method originally? It's just as good as other methods but I don't think many students learn it in school for some reason.

I've seen it thought of as turning the original quadratic into a disguised quadratic by multiplying it by .

But this is just another way of thinking about exactly the same thing.
5. (Original post by Notnek)
Out of interest, were you taught this method originally? It's just as good as other methods but I don't think many students learn it in school for some reason.

I've seen it thought of as turning the original quadratic into a disguised quadratic by multiplying it by .

But this is just another way of thinking about exactly the same thing.
Don't remember being taught a concrete, simple, and easy to remember method in school to be honest. For this, I just googled some simple method and stuck to it.

Though I do prefer your method as it's much faster in practice. I don't factorise quadratics as much anymore to have looked for any simpler method aha
6. (Original post by RDKGames)
Don't remember being taught a concrete, simple, and easy to remember method in school to be honest. For this, I just googled some simple method and stuck to it.

Though I do prefer your method as it's much faster in practice. I don't factorise quadratics as much anymore to have looked for any simpler method aha
Haha yes you don't really have to factorise many quadratics in a maths degree

My method has always been to write out two brackets e.g. (3x + __)(x + __) and work out the missing numbers. But this takes practice so I understand why a lot of students don't like it.

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